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Boklund TI, Snyder J, Gudmand-Hoeyer J, Larsen MK, Knudsen TA, Eickhardt-Dalbøge CS, Skov V, Kjær L, Hasselbalch HC, Andersen M, Ottesen JT, Stiehl T. Mathematical modelling of stem and progenitor cell dynamics during ruxolitinib treatment of patients with myeloproliferative neoplasms. Front Immunol 2024; 15:1384509. [PMID: 38846951 PMCID: PMC11154009 DOI: 10.3389/fimmu.2024.1384509] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2024] [Accepted: 03/27/2024] [Indexed: 06/09/2024] Open
Abstract
Introduction The Philadelphia chromosome-negative myeloproliferative neoplasms are a group of slowly progressing haematological malignancies primarily characterised by an overproduction of myeloid blood cells. Patients are treated with various drugs, including the JAK1/2 inhibitor ruxolitinib. Mathematical modelling can help propose and test hypotheses of how the treatment works. Materials and methods We present an extension of the Cancitis model, which describes the development of myeloproliferative neoplasms and their interactions with inflammation, that explicitly models progenitor cells and can account for treatment with ruxolitinib through effects on the malignant stem cell response to cytokine signalling and the death rate of malignant progenitor cells. The model has been fitted to individual patients' data for the JAK2 V617F variant allele frequency from the COMFORT-II and RESPONSE studies for patients who had substantial reductions (20 percentage points or 90% of the baseline value) in their JAK2 V617F variant allele frequency (n = 24 in total). Results The model fits very well to the patient data with an average root mean square error of 0.0249 (2.49%) when allowing ruxolitinib treatment to affect both malignant stem and progenitor cells. This average root mean square error is much lower than if allowing ruxolitinib treatment to affect only malignant stem or only malignant progenitor cells (average root mean square errors of 0.138 (13.8%) and 0.0874 (8.74%), respectively). Discussion Systematic simulation studies and fitting of the model to the patient data suggest that an initial reduction of the malignant cell burden followed by a monotonic increase can be recapitulated by the model assuming that ruxolitinib affects only the death rate of malignant progenitor cells. For patients exhibiting a long-term reduction of the malignant cells, the model predicts that ruxolitinib also affects stem cell parameters, such as the malignant stem cells' response to cytokine signalling.
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Affiliation(s)
- Tobias Idor Boklund
- Centre for Mathematical Modeling - Human Health and Disease, IMFUFA, Department of Science and Environment, Roskilde University, Roskilde, Denmark
| | - Jordan Snyder
- Centre for Mathematical Modeling - Human Health and Disease, IMFUFA, Department of Science and Environment, Roskilde University, Roskilde, Denmark
| | - Johanne Gudmand-Hoeyer
- Centre for Mathematical Modeling - Human Health and Disease, IMFUFA, Department of Science and Environment, Roskilde University, Roskilde, Denmark
| | | | - Trine Alma Knudsen
- Department of Hematology, Zealand University Hospital, Roskilde, Denmark
| | | | - Vibe Skov
- Department of Hematology, Zealand University Hospital, Roskilde, Denmark
| | - Lasse Kjær
- Department of Hematology, Zealand University Hospital, Roskilde, Denmark
| | | | - Morten Andersen
- Centre for Mathematical Modeling - Human Health and Disease, IMFUFA, Department of Science and Environment, Roskilde University, Roskilde, Denmark
| | - Johnny T. Ottesen
- Centre for Mathematical Modeling - Human Health and Disease, IMFUFA, Department of Science and Environment, Roskilde University, Roskilde, Denmark
| | - Thomas Stiehl
- Centre for Mathematical Modeling - Human Health and Disease, IMFUFA, Department of Science and Environment, Roskilde University, Roskilde, Denmark
- Institute for Computational Biomedicine and Disease Modeling, RWTH Aachen University, Aachen, Germany
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Deutscher K, Hillen T, Newby J. A computational model for the cancer field effect. Front Artif Intell 2023; 6:1060879. [PMID: 37469932 PMCID: PMC10352683 DOI: 10.3389/frai.2023.1060879] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2022] [Accepted: 06/05/2023] [Indexed: 07/21/2023] Open
Abstract
Introduction The Cancer Field Effect describes an area of pre-cancerous cells that results from continued exposure to carcinogens. Cells in the cancer field can easily develop into cancer. Removal of the main tumor mass might leave the cancer field behind, increasing risk of recurrence. Methods The model we propose for the cancer field effect is a hybrid cellular automaton (CA), which includes a multi-layer perceptron (MLP) to compute the effects of the carcinogens on the gene expression of the genes related to cancer development. We use carcinogen interactions that are typically associated with smoking and alcohol consumption and their effect on cancer fields of the tongue. Results Using simulations we support the understanding that tobacco smoking is a potent carcinogen, which can be reinforced by alcohol consumption. The effect of alcohol alone is significantly less than the effect of tobacco. We further observe that pairing tumor excision with field removal delays recurrence compared to tumor excision alone. We track cell lineages and find that, in most cases, a polyclonal field develops, where the number of distinct cell lineages decreases over time as some lineages become dominant over others. Finally, we find tumor masses rarely form via monoclonal origin.
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YILDIZ TUĞBAAKMAN, KÖSE EMEK, ELLIOTT SAMANTHAL. MATHEMATICAL MODELING OF PANCREATIC CANCER TREATMENT WITH CANCER STEM CELLS. J BIOL SYST 2021. [DOI: 10.1142/s0218339021500182] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Of all cancers, pancreatic cancer has a significantly low rate of survival, mostly due to lack of early screening. Thus, once detected, pancreatic cancer is usually in later stages, reducing the likelihood of full recovery. The most common treatment strategy is chemotherapy, although several immunotherapeutic drugs show promising results in extending the patient’s lifespan. In this paper, we provide a validated mathematical model for the pancreatic cancer after fitting the parameter values, such as tumor growth rate, inverse carrying capacity, activation and decay rate of pancreatic stellate cells, with the use of the experimental data presented by Cioffi et al. cioffi2015inhibition For treatments with the chemotherapeutic drugs, Abraxane and Gemcitabine, and the immunotherapeutic drug, Anti-CD47, we modified the model accurately and compared the simulation results with the experimental data not only to model pancreatic cancer treatment correctly but also to move forward with other drug trials. Then, we include the cancer stem cells, which are known to initiate tumors and cause a relapse post-chemotherapy, per cancer stem cell hypothesis so that cancer progression can be assessed based on this phenomenon. In addition, we investigate optimal drug protocols. We find out that the most effective treatment is dual therapy due to extending survival time when compared to other drugs. Moreover, this study reveals that drug dose is more effectual than frequency of drug injection on account of different treatment scheduling with the same dose over a week. The model could be a starting point to investigate pancreatic cancer progression based on cancer stem cell hypothesis and shed light on novel drug discoveries.
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Affiliation(s)
- TUĞBA AKMAN YILDIZ
- Department of Computer Engineering, University of Turkish Aeronautical Association, 06790 Ankara, Turkey
| | - EMEK KÖSE
- Department of Mathematics and Computer Science, St. Mary’s College of Maryland, St. Mary’s City, MD 20619, USA
| | - SAMANTHA L. ELLIOTT
- Department of Biology, St. Mary’s College of Maryland, St. Mary’s City, MD 20619, USA
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Ottesen JT, Andersen M. Potential of Immunotherapies in Treating Hematological Cancer-Infection Comorbidities-A Mathematical Modelling Approach. Cancers (Basel) 2021; 13:3789. [PMID: 34359690 PMCID: PMC8345105 DOI: 10.3390/cancers13153789] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2021] [Revised: 07/08/2021] [Accepted: 07/23/2021] [Indexed: 11/17/2022] Open
Abstract
BACKGROUND The immune system attacks threats like an emerging cancer or infections like COVID-19 but it also plays a role in dealing with autoimmune disease, e.g., inflammatory bowel diseases, and aging. Malignant cells may tend to be eradicated, to appraoch a dormant state or escape the immune system resulting in uncontrolled growth leading to cancer progression. If the immune system is busy fighting a cancer, a severe infection on top of it may compromise the immunoediting and the comorbidity may be too taxing for the immune system to control. METHOD A novel mechanism based computational model coupling a cancer-infection development to the adaptive immune system is presented and analyzed. The model maps the outcome to the underlying physiological mechanisms and agree with numerous evidence based medical observations. RESULTS AND CONCLUSIONS Progression of a cancer and the effect of treatments depend on the cancer size, the level of infection, and on the efficiency of the adaptive immune system. The model exhibits bi-stability, i.e., virtual patient trajectories gravitate towards one of two stable steady states: a dormant state or a full-blown cancer-infection disease state. An infectious threshold curve exists and if infection exceed this separatrix for sufficiently long time the cancer escapes. Thus, early treatment is vital for remission and severe infections may instigate cancer progression. CAR T-cell Immunotherapy may sufficiently control cancer progression back into a dormant state but the therapy significantly gains efficiency in combination with antibiotics or immunomodulation.
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Affiliation(s)
- Johnny T. Ottesen
- Center for Mathematical Modeling-Human Health and Disease (COMMAND), Roskilde University, 4000 Roskilde, Denmark;
- IMFUFA, Department of Science and Environment, Roskilde University, 4000 Roskilde, Denmark
| | - Morten Andersen
- Center for Mathematical Modeling-Human Health and Disease (COMMAND), Roskilde University, 4000 Roskilde, Denmark;
- IMFUFA, Department of Science and Environment, Roskilde University, 4000 Roskilde, Denmark
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Batool I, Bajcinca N. Evolution of cancer stem cell lineage involving feedback regulation. PLoS One 2021; 16:e0251481. [PMID: 34014979 PMCID: PMC8136751 DOI: 10.1371/journal.pone.0251481] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2020] [Accepted: 04/27/2021] [Indexed: 01/16/2023] Open
Abstract
Tumor emergence and progression is a complex phenomenon that assumes special molecular and cellular interactions. The hierarchical structuring and communication via feedback signaling of different cell types, which are categorized as the stem, progenitor, and differentiated cells in dependence of their maturity level, plays an important role. Under healthy conditions, these cells build a dynamical system that is responsible for facilitating the homeostatic regulation of the tissue. Generally, in this hierarchical setting, stem and progenitor cells are yet likely to undergo a mutation, when a cell divides into two daughter cells. This may lead to the development of abnormal characteristics, i.e. mutation in the cell, yielding an unrestrained number of cells. Therefore, the regulation of a stem cell’s proliferation and differentiation rate is crucial for maintaining the balance in the overall cell population. In this paper, a maturity based mathematical model with feedback regulation is formulated for healthy and mutated cell lineages. It is given in the form of coupled ordinary and partial differential equations. The focus is laid on the dynamical effects resulting from acquiring a mutation in the hierarchical structure of stem, progenitor and fully differentiated cells. Additionally, the effects of nonlinear feedback regulation from mature cells into both stem and progenitor cell populations have been inspected. The steady-state solutions of the model are derived analytically. Numerical simulations and results based on a finite volume scheme underpin various expected behavioral patterns of the homeostatic regulation and cancer evolution. For instance, it has been found that the mutated cells can experience significant growth even with a single somatic mutation, but under homeostatic regulation acquire a steady-state and thus, ensuing healthy cell population to either a steady-state or a lower cell concentration. Furthermore, the model behavior has been validated with different experimentally measured tumor values from the literature.
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Affiliation(s)
- Iqra Batool
- Faculty of Mechanical and Process Engineering, Technische Universität Kaiserslautern, Kaiserslautern, Rheinland Pfalz, Germany
| | - Naim Bajcinca
- Faculty of Mechanical and Process Engineering, Technische Universität Kaiserslautern, Kaiserslautern, Rheinland Pfalz, Germany
- * E-mail:
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Andersen M, Hasselbalch HC, Kjær L, Skov V, Ottesen JT. Global dynamics of healthy and cancer cells competing in the hematopoietic system. Math Biosci 2020; 326:108372. [PMID: 32442449 DOI: 10.1016/j.mbs.2020.108372] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2019] [Revised: 05/06/2020] [Accepted: 05/06/2020] [Indexed: 01/08/2023]
Abstract
Stem cells in the bone marrow differentiate to ultimately become mature, functioning blood cells through a tightly regulated process (hematopoiesis) including a stem cell niche interaction and feedback through the immune system. Mutations in a hematopoietic stem cell can create a cancer stem cell leading to a less controlled production of malfunctioning cells in the hematopoietic system. This was mathematically modelled by Andersen et al. (2017) including the dynamic variables: healthy and cancer stem cells and mature cells, dead cells and an immune system response. Here, we apply a quasi steady state approximation to this model to construct a two dimensional model with four algebraic equations denoted the simple cancitis model. The two dynamic variables are the clinically available quantities JAK2V617F allele burden and the number of white blood cells. The simple cancitis model represents the original model very well. Complete phase space analysis of the simple cancitis model is performed, including proving the existence and location of globally attracting steady states. Hence, parameter values from compartments of stem cells, mature cells and immune cells are directly linked to disease and treatment prognosis, showing the crucial importance of early intervention. The simple cancitis model allows for a complete analysis of the long term evolution of trajectories. In particular, the value of the self renewal of the hematopoietic stem cells divided by the self renewal of the cancer stem cells is found to be an important diagnostic marker and perturbing this parameter value at intervention allows the model to reproduce clinical data. Treatment at low cancer cell numbers allows returning to healthy blood production while the same intervention at a later disease stage can lead to eradication of healthy blood producing cells. Assuming the total number of white blood cells is constant in the early cancer phase while the allele burden increases, a one dimensional model is suggested and explicitly solved, including parameters from all original compartments. The solution explicitly shows that exogenous inflammation promotes blood cancer when cancer stem cells reproduce more efficiently than hematopoietic stem cells.
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Affiliation(s)
- Morten Andersen
- IMFUFA, Department of Science and Environment, Roskilde University, Denmark.
| | - Hans C Hasselbalch
- Department of Haematology, Zealand University Hospital, Roskilde, Denmark
| | - Lasse Kjær
- Department of Haematology, Zealand University Hospital, Roskilde, Denmark
| | - Vibe Skov
- Department of Haematology, Zealand University Hospital, Roskilde, Denmark
| | - Johnny T Ottesen
- IMFUFA, Department of Science and Environment, Roskilde University, Denmark
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Maddalena L, Ragni S. Existence of solutions and numerical approximation of a non-local tumor growth model. MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA 2020; 37:58-82. [PMID: 30933283 DOI: 10.1093/imammb/dqz005] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2018] [Revised: 02/01/2019] [Accepted: 02/26/2019] [Indexed: 11/15/2022]
Abstract
In order to model the evolution of a heterogeneous population of cancer stem cells and tumor cells, we analyse a nonlinear system of integro-differential equations. We provide an existence and uniqueness result by exploiting a suitable iterative scheme of functions which converge to the solution of the system. Then, we discretize the model and perform some numerical simulations. Numerical approximations are obtained by applying finite differences for space discretization and an exponential Runge-Kutta scheme for time integration. We exploit the numerical tool in order to investigate the effects that niches have on cancer development. In this respect, the numerical procedure is applied in the case when the function of cell redistribution is assumed to be spatially explicit. It allows for finding an approximate solution which is spatially inhomogeneous as time progresses. In this framework, numerical investigation may help in understanding the process of niche construction, which plays an important role in cancer population biology.
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Affiliation(s)
- Lucia Maddalena
- Department of Economics, University of Foggia, Largo Papa Giovanni Paolo II, Foggia, Italy
| | - Stefania Ragni
- Department of Economics and Management, University of Ferrara, Via Voltapaletto, Ferrara, Italy
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8
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Pirastehzad A, Taghizadeh A, Jamshidi AA. The formation of cancer stem cells in EMT6/Ro tumor: Hybrid modeling within its micro-environment. INFORMATICS IN MEDICINE UNLOCKED 2020. [DOI: 10.1016/j.imu.2019.100247] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022] Open
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9
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Teimouri H, Kochugaeva MP, Kolomeisky AB. Elucidating the correlations between cancer initiation times and lifetime cancer risks. Sci Rep 2019; 9:18940. [PMID: 31831779 PMCID: PMC6908632 DOI: 10.1038/s41598-019-55300-w] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2019] [Accepted: 11/26/2019] [Indexed: 12/29/2022] Open
Abstract
Cancer is a genetic disease that results from accumulation of unfavorable mutations. As soon as genetic and epigenetic modifications associated with these mutations become strong enough, the uncontrolled tumor cell growth is initiated, eventually spreading through healthy tissues. Clarifying the dynamics of cancer initiation is thus critically important for understanding the molecular mechanisms of tumorigenesis. Here we present a new theoretical method to evaluate the dynamic processes associated with the cancer initiation. It is based on a discrete-state stochastic description of the formation of tumors as a fixation of cancerous mutations in tissues. Using a first-passage analysis the probabilities for the cancer to appear and the times before it happens, which are viewed as fixation probabilities and fixation times, respectively, are explicitly calculated. It is predicted that the slowest cancer initiation dynamics is observed for neutral mutations, while it is fast for both advantageous and, surprisingly, disadvantageous mutations. The method is applied for estimating the cancer initiation times from experimentally available lifetime cancer risks for different types of cancer. It is found that the higher probability of the cancer to occur does not necessary lead to the faster times of starting the cancer. Our theoretical analysis helps to clarify microscopic aspects of cancer initiation processes.
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Affiliation(s)
- Hamid Teimouri
- Department of Chemistry, Rice University, Houston, TX, United States
- Center for Theoretical Biological Physics, Rice University, Houston, TX, United States
| | - Maria P Kochugaeva
- Department of Biomedical Engineering and Systems Biology Institute, Yale University, West Haven, CT, United States
| | - Anatoly B Kolomeisky
- Department of Chemistry, Rice University, Houston, TX, United States.
- Center for Theoretical Biological Physics, Rice University, Houston, TX, United States.
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, TX, United States.
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10
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Fassoni AC, Yang HM. Modeling dynamics for oncogenesis encompassing mutations and genetic instability. MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA 2019; 36:241-267. [PMID: 29947770 DOI: 10.1093/imammb/dqy010] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2016] [Revised: 05/31/2018] [Accepted: 06/08/2018] [Indexed: 12/29/2022]
Abstract
Tumorigenesis has been described as a multistep process, where each step is associated with a genetic alteration, in the direction to progressively transform a normal cell and its descendants into a malignant tumour. Into this work, we propose a mathematical model for cancer onset and development, considering three populations: normal, premalignant and cancer cells. The model takes into account three hallmarks of cancer: self-sufficiency on growth signals, insensibility to anti-growth signals and evading apoptosis. By using a nonlinear expression to describe the mutation from premalignant to cancer cells, the model includes genetic instability as an enabling characteristic of tumour progression. Mathematical analysis was performed in detail. Results indicate that apoptosis and tissue repair system are the first barriers against tumour progression. One of these mechanisms must be corrupted for cancer to develop from a single mutant cell. The results also show that the presence of aggressive cancer cells opens way to survival of less adapted premalignant cells. Numerical simulations were performed with parameter values based on experimental data of breast cancer, and the necessary time taken for cancer to reach a detectable size from a single mutant cell was estimated with respect to some parameters. We find that the rates of apoptosis and mutations have a large influence on the pace of tumour progression and on the time it takes to become clinically detectable.
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Affiliation(s)
- Artur C Fassoni
- Instituto de Matemática e Computação, UNIFEI, Itajubá, Minas Gerais, Brazil
| | - Hyun M Yang
- Instituto de Matemática, Estatística e Computação Científica, UNICAMP, Campinas, São Paulo, Brazil
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Stiehl T, Marciniak-Czochra A. How to Characterize Stem Cells? Contributions from Mathematical Modeling. CURRENT STEM CELL REPORTS 2019. [DOI: 10.1007/s40778-019-00155-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
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12
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Peitzsch C, Nathansen J, Schniewind SI, Schwarz F, Dubrovska A. Cancer Stem Cells in Head and Neck Squamous Cell Carcinoma: Identification, Characterization and Clinical Implications. Cancers (Basel) 2019; 11:cancers11050616. [PMID: 31052565 PMCID: PMC6562868 DOI: 10.3390/cancers11050616] [Citation(s) in RCA: 51] [Impact Index Per Article: 10.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2019] [Revised: 04/21/2019] [Accepted: 04/26/2019] [Indexed: 12/19/2022] Open
Abstract
Head and neck squamous cell carcinoma (HNSCC) is the sixth most commonly diagnosed cancer worldwide. Despite advances in the treatment management, locally advanced disease has a poor prognosis, with a 5-year survival rate of approximately 50%. The growth of HNSCC is maintained by a population of cancer stem cells (CSCs) which possess unlimited self-renewal potential and induce tumor regrowth if not completely eliminated by therapy. The population of CSCs is not only a promising target for tumor treatment, but also an important biomarker to identify the patients at risk for therapeutic failure and disease progression. This review aims to provide an overview of the recent pre-clinical and clinical studies on the biology and potential therapeutic implications of HNSCC stem cells.
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Affiliation(s)
- Claudia Peitzsch
- National Center for Tumor Diseases (NCT), Partner Site Dresden, Germany: German Cancer Research Center (DKFZ), Heidelberg, Germany.
- OncoRay-National Center for Radiation Research in Oncology, Faculty of Medicine and University Hospital Carl Gustav Carus, Technische Universität Dresden, 01307 Dresden, Germany.
- German Cancer Consortium (DKTK), Partner site Dresden, 01307 Dresden, Germany.
| | - Jacqueline Nathansen
- OncoRay-National Center for Radiation Research in Oncology, Faculty of Medicine and University Hospital Carl Gustav Carus, Technische Universität Dresden, 01307 Dresden, Germany.
| | - Sebastian I Schniewind
- OncoRay-National Center for Radiation Research in Oncology, Faculty of Medicine and University Hospital Carl Gustav Carus, Technische Universität Dresden, 01307 Dresden, Germany.
| | - Franziska Schwarz
- OncoRay-National Center for Radiation Research in Oncology, Faculty of Medicine and University Hospital Carl Gustav Carus, Technische Universität Dresden, 01307 Dresden, Germany.
- German Cancer Consortium (DKTK), Partner site Dresden, 01307 Dresden, Germany.
- Helmholtz-Zentrum Dresden-Rossendorf, Institute of Radiooncology-OncoRay, 01307 Dresden, Germany.
| | - Anna Dubrovska
- OncoRay-National Center for Radiation Research in Oncology, Faculty of Medicine and University Hospital Carl Gustav Carus, Technische Universität Dresden, 01307 Dresden, Germany.
- German Cancer Consortium (DKTK), Partner site Dresden, 01307 Dresden, Germany.
- Helmholtz-Zentrum Dresden-Rossendorf, Institute of Radiooncology-OncoRay, 01307 Dresden, Germany.
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Afenya EK, Ouifki R, Mundle SD. Mathematical modeling of bone marrow - peripheral blood dynamics in the disease state based on current emerging paradigms, part II. J Theor Biol 2019; 460:37-55. [PMID: 30296448 DOI: 10.1016/j.jtbi.2018.10.008] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2017] [Revised: 09/28/2018] [Accepted: 10/01/2018] [Indexed: 12/31/2022]
Abstract
The cancer stem cell hypothesis has gained currency in recent times but concerns remain about its scientific foundations because of significant gaps that exist between research findings and comprehensive knowledge about cancer stem cells (CSCs). In this light, a mathematical model that considers hematopoietic dynamics in the diseased state of the bone marrow and peripheral blood is proposed and used to address findings about CSCs. The ensuing model, resulting from a modification and refinement of a recent model, develops out of the position that mathematical models of CSC development, that are few at this time, are needed to provide insightful underpinnings for biomedical findings about CSCs as the CSC idea gains traction. Accordingly, the mathematical challenges brought on by the model that mirror general challenges in dealing with nonlinear phenomena are discussed and placed in context. The proposed model describes the logical occurrence of discrete time delays, that by themselves present mathematical challenges, in the evolving cell populations under consideration. Under the challenging circumstances, the steady state properties of the model system of delay differential equations are obtained, analyzed, and the resulting mathematical predictions arising therefrom are interpreted and placed within the framework of findings regarding CSCs. Simulations of the model are carried out by considering various parameter scenarios that reflect different experimental situations involving disease evolution in human hosts. Model analyses and simulations suggest that the emergence of the cancer stem cell population alongside other malignant cells engenders higher dimensions of complexity in the evolution of malignancy in the bone marrow and peripheral blood at the expense of healthy hematopoietic development. The model predicts the evolution of an aberrant environment in which the malignant population particularly in the bone marrow shows tendencies of reaching an uncontrollable equilibrium state. Essentially, the model shows that a structural relationship exists between CSCs and non-stem malignant cells that confers on CSCs the role of temporally enhancing and stimulating the expansion of non-stem malignant cells while also benefitting from increases in their own population and these CSCs may be the main protagonists that drive the ultimate evolution of the uncontrollable equilibrium state of such malignant cells and these may have implications for treatment.
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Affiliation(s)
- Evans K Afenya
- Department of Mathematics, Elmhurst College, 190 Prospect Avenue, Elmhurst, IL 60126, USA.
| | - Rachid Ouifki
- Department of Mathematics and Applied Mathematics, University of Pretoria, South Africa.
| | - Suneel D Mundle
- Department of Biochemistry, Rush University Medical Center, 1735 W. Harrison St, Chicago, IL 60612, USA.
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Ottesen JT, Pedersen RK, Sajid Z, Gudmand-Hoeyer J, Bangsgaard KO, Skov V, Kjær L, Knudsen TA, Pallisgaard N, Hasselbalch HC, Andersen M. Bridging blood cancers and inflammation: The reduced Cancitis model. J Theor Biol 2019; 465:90-108. [PMID: 30615883 DOI: 10.1016/j.jtbi.2019.01.001] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2018] [Revised: 12/11/2018] [Accepted: 01/02/2019] [Indexed: 11/28/2022]
Abstract
A novel mechanism-based model - the Cancitis model - describing the interaction of blood cancer and the inflammatory system is proposed, analyzed and validated. The immune response is divided into two components, one where the elimination rate of malignant stem cells is independent of the level of the blood cancer and one where the elimination rate depends on the level of the blood cancer. A dimensional analysis shows that the full 6-dimensional system of nonlinear ordinary differential equations may be reduced to a 2-dimensional system - the reduced Cancitis model - using Fenichel theory. The original 18 parameters appear in the reduced model in 8 groups of parameters. The reduced model is analyzed. Especially the steady states and their dependence on the exogenous inflammatory stimuli are analyzed. A semi-analytic investigation reveals the stability properties of the steady states. Finally, positivity of the system and the existence of an attracting trapping region in the positive octahedron guaranteeing global existence and uniqueness of solutions are proved. The possible topologies of the dynamical system are completely determined as having a Janus structure, where two qualitatively different topologies appear for different sets of parameters. To classify this Janus structure we propose a novel concept in blood cancer - a reproduction ratio R. It determines the topological structure depending on whether it is larger or smaller than a threshold value. Furthermore, it follows that inflammation, affected by the exogenous inflammatory stimulation, may determine the onset and development of blood cancers. The body may manage initial blood cancer as long as the self-renewal rate is not too high, but fails to manage it if an inflammation appears. Thus, inflammation may trigger and drive blood cancers. Finally, the mathematical analysis suggests novel treatment strategies and it is used to discuss the in silico effect of existing treatment, e.g. interferon-α or T-cell therapy, and the impact of malignant cells becoming resistant.
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Affiliation(s)
- Johnny T Ottesen
- Department of Science and Environment, Roskilde University, Denmark.
| | | | - Zamra Sajid
- Department of Science and Environment, Roskilde University, Denmark
| | | | | | - Vibe Skov
- Department of Hematology, Zealand University Hospital, University of Copenhagen, Denmark
| | - Lasse Kjær
- Department of Hematology, Zealand University Hospital, University of Copenhagen, Denmark
| | - Trine A Knudsen
- Department of Hematology, Zealand University Hospital, University of Copenhagen, Denmark
| | - Niels Pallisgaard
- Department of Hematology, Zealand University Hospital, University of Copenhagen, Denmark
| | - Hans C Hasselbalch
- Department of Hematology, Zealand University Hospital, University of Copenhagen, Denmark
| | - Morten Andersen
- Department of Science and Environment, Roskilde University, Denmark
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15
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Minussi DC, Henz B, Dos Santos Oliveira M, Filippi-Chiela EC, Oliveira MM, Lenz G. esiCancer: Evolutionary In Silico Cancer Simulator. Cancer Res 2018; 79:1010-1013. [PMID: 30563892 DOI: 10.1158/0008-5472.can-17-3924] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2017] [Revised: 09/18/2018] [Accepted: 12/14/2018] [Indexed: 11/16/2022]
Abstract
The evolution of cancer is inferred mainly from samples taken at discrete points that represent glimpses of the complete process. In this study, we present esiCancer as a cancer-evolution simulator. It uses a branching process, randomly applying events to a diploid oncogenome, altering probabilities of proliferation and death of the affected cells. Multiple events that occur over hundreds of generations may lead to a gradual change in cell fitness and the establishment of a fast-growing population. esiCancer provides a platform to study the impact of several factors on tumor evolution, including dominance, fitness, event rate, and interactions among genes as well as factors affecting the tumor microenvironment. The output of esiCancer can be used to reconstruct clonal composition and Kaplan-Meier-like survival curves of multiple evolutionary stories. esiCancer is an open-source, standalone software to model evolutionary aspects of cancer biology. SIGNIFICANCE: This study provides a customizable and hands-on simulation tool to model the effect of diverse types of genomic alterations on the fate of tumor cells.
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Affiliation(s)
- Darlan Conterno Minussi
- Departamento de Biofísica, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Rio Grande do Sul, Brazil.,Centro de Biotecnologia, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Rio Grande do Sul, Brazil
| | - Bernardo Henz
- Instituto de Informática, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Rio Grande do Sul, Brazil
| | - Mariana Dos Santos Oliveira
- Departamento de Biofísica, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Rio Grande do Sul, Brazil.,Centro de Biotecnologia, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Rio Grande do Sul, Brazil
| | - Eduardo C Filippi-Chiela
- Departamento de Ciências Morfológicas, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Rio Grande do Sul, Brazil
| | - Manuel M Oliveira
- Instituto de Informática, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Rio Grande do Sul, Brazil
| | - Guido Lenz
- Departamento de Biofísica, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Rio Grande do Sul, Brazil. .,Centro de Biotecnologia, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Rio Grande do Sul, Brazil
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16
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Van Roten A, Barakat AZAZ, Wouters A, Tran TA, Mouton S, Noben JP, Gentile L, Smeets K. A carcinogenic trigger to study the function of tumor suppressor genes in Schmidtea mediterranea. Dis Model Mech 2018; 11:dmm032573. [PMID: 29967069 PMCID: PMC6176991 DOI: 10.1242/dmm.032573] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2017] [Accepted: 06/25/2018] [Indexed: 12/30/2022] Open
Abstract
Planarians have been long known for their regenerative ability, which hinges on pluripotency. Recently, however, the planarian model has been successfully established for routine toxicological screens aimed to assess overproliferation, mutagenicity and tumorigenesis. In this study, we focused on planarian tumor suppressor genes (TSGs) and their role during chemically induced carcinogenic stress in Schmidtea mediterranea Combining in silico and proteomic screens with exposure to human carcinogen type 1A agent cadmium (Cd), we showed that many TSGs have a function in stem cells and that, in general, exposure to Cd accelerated the onset and increased the severity of the observed phenotype. This suggested that the interaction between environmental and genetic factors plays an important role in tumor development in S. mediterranea Therefore, we further focused on the synergistic effects of Cd exposure and p53 knockdown (KD) at the cellular and molecular levels. Cd also produced a specific proteomic landscape in homeostatic animals, with 172 proteins differentially expressed, 43 of which were downregulated. Several of these proteins have tumor suppressor function in human and other animals, namely Wilms Tumor 1 Associated Protein (WT1), Heat Shock Protein 90 (HSP90), Glioma Pathogenesis-Related Protein 1 (GLIPR1) and Matrix Metalloproteinase B (Smed-MMPB). Both Glipr1 and MmpB KD produced large outgrowths, epidermal lesions and epidermal blisters. The epidermal blisters that formed as a consequence of Smed-MmpB KD were populated by smedwi1+ cells, many of which were actively proliferating, while large outgrowths contained ectopically differentiated structures, such as photoreceptors, nervous tissue and a small pharynx. In conclusion, Smed-MmpB is a planarian TSG that prevents stem cell proliferation and differentiation outside the proper milieu.
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Affiliation(s)
- Andromeda Van Roten
- Zoology: Biodiversity and Toxicology, Hasselt University-Campus Diepenbeek, Agoralaan 1, Gebouw D, 3590, Diepenbeek, Belgium
| | - Amal Zohir Abo-Zeid Barakat
- Planarian Stem Cell Laboratory, Max Planck Institute for Molecular Biomedicine, von Esmarch-str. 54, 48149, Münster, Germany
| | - Annelies Wouters
- Zoology: Biodiversity and Toxicology, Hasselt University-Campus Diepenbeek, Agoralaan 1, Gebouw D, 3590 Diepenbeek, Belgium
| | - Thao Anh Tran
- Pluripotency and Regeneration Group, Fraunhofer Institute for Biomedical Engineering, Joseph-von-Fraunhofer-Weg 1, 66280, Sulzbach, Germany
| | - Stijn Mouton
- European Research Institute for the Biology of Ageing, University Medical Center Groningen, University of Groningen, 9713, Groningen, The Netherlands
| | - Jean-Paul Noben
- Biomedical Research Institute, Hasselt University and Transnationale Universiteit Limburg, School of Life Sciences, 3590, Diepenbeek, Belgium
| | - Luca Gentile
- Planarian Stem Cell Laboratory, Max Planck Institute for Molecular Biomedicine, von Esmarch-str. 54, 48149, Münster, Germany
| | - Karen Smeets
- Zoology: Biodiversity and Toxicology, Hasselt University-Campus Diepenbeek, Agoralaan 1, Gebouw D, 3590, Diepenbeek, Belgium
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17
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Nazari F, Pearson AT, Nör JE, Jackson TL. A mathematical model for IL-6-mediated, stem cell driven tumor growth and targeted treatment. PLoS Comput Biol 2018; 14:e1005920. [PMID: 29351275 PMCID: PMC5792033 DOI: 10.1371/journal.pcbi.1005920] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2017] [Revised: 01/31/2018] [Accepted: 12/10/2017] [Indexed: 12/20/2022] Open
Abstract
Targeting key regulators of the cancer stem cell phenotype to overcome their critical influence on tumor growth is a promising new strategy for cancer treatment. Here we present a modeling framework that operates at both the cellular and molecular levels, for investigating IL-6 mediated, cancer stem cell driven tumor growth and targeted treatment with anti-IL6 antibodies. Our immediate goal is to quantify the influence of IL-6 on cancer stem cell self-renewal and survival, and to characterize the subsequent impact on tumor growth dynamics. By including the molecular details of IL-6 binding, we are able to quantify the temporal changes in fractional occupancies of bound receptors and their influence on tumor volume. There is a strong correlation between the model output and experimental data for primary tumor xenografts. We also used the model to predict tumor response to administration of the humanized IL-6R monoclonal antibody, tocilizumab (TCZ), and we found that as little as 1mg/kg of TCZ administered weekly for 7 weeks is sufficient to result in tumor reduction and a sustained deceleration of tumor growth. A small population of cancer stem cells that share many of the biological characteristics of normal adult stem cells are believed to initiate and sustain tumor growth for a wide variety of malignancies. Growth and survival of these cancer stem cells is highly influenced by tumor micro-environmental factors and molecular signaling initiated by cytokines and growth factors. This work focuses on quantifying the influence of IL-6, a pleiotropic cytokine secreted by a variety of cell types, on cancer stem cell self-renewal and survival. We present a mathematical model for IL-6 mediated, cancer stem cell driven tumor growth that operates at the following levels: (1) the molecular level—capturing cell surface dynamics of receptor-ligand binding and receptor activation that lead to intra-cellular signal transduction cascades; and (2) the cellular level—describing tumor growth, cellular composition, and response to treatments targeted against IL-6.
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Affiliation(s)
- Fereshteh Nazari
- Simon A. Levin Mathematical, Computational, and Modeling Sciences Center, School of Human Evolution and Social Change, Arizona State University, Tempe, Arizona, United States of America
| | - Alexander T. Pearson
- Division of Hematology/Oncology, Department of Internal Medicine, University of Michigan Cancer Center, Ann Arbor, Michigan, United States of America
| | - Jacques Eduardo Nör
- Departments of Cardiology, Restorative Sciences, and Endontics, University of Michigan, Ann Arbor, Michigan, United States of America
| | - Trachette L. Jackson
- Department of Mathematics, University of Michigan, Ann Arbor, Michigan, United States of America
- * E-mail:
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18
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Stem cell self-renewal in regeneration and cancer: Insights from mathematical modeling. ACTA ACUST UNITED AC 2017. [DOI: 10.1016/j.coisb.2017.09.006] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
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19
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Andersen M, Sajid Z, Pedersen RK, Gudmand-Hoeyer J, Ellervik C, Skov V, Kjær L, Pallisgaard N, Kruse TA, Thomassen M, Troelsen J, Hasselbalch HC, Ottesen JT. Mathematical modelling as a proof of concept for MPNs as a human inflammation model for cancer development. PLoS One 2017; 12:e0183620. [PMID: 28859112 PMCID: PMC5578482 DOI: 10.1371/journal.pone.0183620] [Citation(s) in RCA: 42] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2017] [Accepted: 08/08/2017] [Indexed: 12/15/2022] Open
Abstract
The chronic Philadelphia-negative myeloproliferative neoplasms (MPNs) are acquired stem cell neoplasms which ultimately may transform to acute myelogenous leukemia. Most recently, chronic inflammation has been described as an important factor for the development and progression of MPNs in the biological continuum from early cancer stage to the advanced myelofibrosis stage, the MPNs being described as "A Human Inflammation Model for Cancer Development". This novel concept has been built upon clinical, experimental, genomic, immunological and not least epidemiological studies. Only a few studies have described the development of MPNs by mathematical models, and none have addressed the role of inflammation for clonal evolution and disease progression. Herein, we aim at using mathematical modelling to substantiate the concept of chronic inflammation as an important trigger and driver of MPNs.The basics of the model describe the proliferation from stem cells to mature cells including mutations of healthy stem cells to become malignant stem cells. We include a simple inflammatory coupling coping with cell death and affecting the basic model beneath. First, we describe the system without feedbacks or regulatory interactions. Next, we introduce inflammatory feedback into the system. Finally, we include other feedbacks and regulatory interactions forming the inflammatory-MPN model. Using mathematical modeling, we add further proof to the concept that chronic inflammation may be both a trigger of clonal evolution and an important driving force for MPN disease progression. Our findings support intervention at the earliest stage of cancer development to target the malignant clone and dampen concomitant inflammation.
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Affiliation(s)
- Morten Andersen
- Department of Science and Environment, Roskilde University, Roskilde, Denmark
| | - Zamra Sajid
- Department of Science and Environment, Roskilde University, Roskilde, Denmark
| | - Rasmus K. Pedersen
- Department of Science and Environment, Roskilde University, Roskilde, Denmark
| | | | - Christina Ellervik
- Department of Laboratory Medicine at Boston Children’s Hospital, Boston, Massachusetts, United States of America
| | - Vibe Skov
- Department of Hematology, Zealand University Hospital, University of Copenhagen, Roskilde, Denmark
| | - Lasse Kjær
- Department of Hematology, Zealand University Hospital, University of Copenhagen, Roskilde, Denmark
| | - Niels Pallisgaard
- Department of Pathology, Zealand University Hospital, University of Copenhagen, Roskilde, Denmark
| | - Torben A. Kruse
- Department of Clinical Genetics, Odense University Hospital, Odense, Denmark
| | - Mads Thomassen
- Department of Clinical Genetics, Odense University Hospital, Odense, Denmark
| | - Jesper Troelsen
- Department of Science and Environment, Roskilde University, Roskilde, Denmark
| | - Hans Carl Hasselbalch
- Department of Hematology, Zealand University Hospital, University of Copenhagen, Roskilde, Denmark
| | - Johnny T. Ottesen
- Department of Science and Environment, Roskilde University, Roskilde, Denmark
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20
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21
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Shimura M, Szyrwiel L, Matsuyama S, Yamauchi K. Visualization of Intracellular Elements Using Scanning X-Ray Fluorescence Microscopy. Metallomics 2017. [DOI: 10.1007/978-4-431-56463-8_3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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22
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Pearson AT, Jackson TL, Nör JE. Modeling head and neck cancer stem cell-mediated tumorigenesis. Cell Mol Life Sci 2016; 73:3279-89. [PMID: 27151511 PMCID: PMC5312795 DOI: 10.1007/s00018-016-2226-x] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2015] [Revised: 03/29/2016] [Accepted: 04/12/2016] [Indexed: 12/22/2022]
Abstract
A large body of literature has emerged supporting the importance of cancer stem cells (CSCs) in the pathogenesis of head and neck cancers. CSCs are a subpopulation of cells within a tumor that share the properties of self-renewal and multipotency with stem cells from normal tissue. Their functional relevance to the pathobiology of cancer arises from the unique properties of tumorigenicity, chemotherapy resistance, and their ability to metastasize and invade distant tissues. Several molecular profiles have been used to discriminate a stem cell from a non-stem cell. CSCs can be grown for study and further enriched using a number of in vitro techniques. An evolving option for translational research is the use of mathematical and computational models to describe the role of CSCs in complex tumor environments. This review is focused discussing the evidence emerging from modeling approaches that have clarified the impact of CSCs to the biology of cancer.
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Affiliation(s)
- Alexander T Pearson
- Division of Hematology/Oncology, Department of Internal Medicine, University of Michigan School of Medicine, 1500 E. Medical Center Dr., SPC 5848, Ann Arbor, MI, 48109-5848, USA.
| | - Trachette L Jackson
- Department of Mathematics, University of Michigan School of Literature, Sciences, and the Arts, Ann Arbor, MI, USA
| | - Jacques E Nör
- Department of Restorative Sciences, University of Michigan School of Dentistry, 1011 N. University Rm. 2309, Ann Arbor, MI, 48109-1078, USA.
- Department of Otolaryngology, University of Michigan School of Medicine, Ann Arbor, MI, USA.
- Department of Biomedical Engineering, University of Michigan College of Engineering, Ann Arbor, MI, USA.
- Comprehensive Cancer Center, University of Michigan, Ann Arbor, MI, USA.
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23
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Marcu LG, Marcu D, Filip SM. In silico study of the impact of cancer stem cell dynamics and radiobiological hypoxia on tumour response to hyperfractionated radiotherapy. Cell Prolif 2016; 49:304-14. [PMID: 27079860 DOI: 10.1111/cpr.12251] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2016] [Accepted: 02/10/2016] [Indexed: 02/05/2023] Open
Abstract
OBJECTIVES Advanced head and neck carcinomas (HNCs) are aggressive tumours, mainly due to hypoxia and a cancer stem cell (CSC) subpopulation. The aim of this study was to simulate tumour growth and behaviour during radiotherapy of three HNC groups (governed by different growth kinetics, hypoxia levels and CSC division pattern) to determine correlation between resistance factors and responses to hyperfractionated radiotherapy. METHODS An in silico HNC model was developed based on biologically realistic input parameters. During radiotherapy simulation, three parameters were studied: growth kinetics, hypoxia and probability of CSC symmetrical division. Both independent and combined effects on tumour response to hyperfractionated radiotherapy were assessed. RESULTS Oxic and very mildly hypoxic HNCs were revealed to be controlled by hyperfractionated radiotherapy, irrespective of growth kinetics and CSC division pattern. Moderately hypoxic tumours had different responses to radiotherapy: while slowly proliferating HNCs were still controllable, tumours with higher cell turnover were more resistant. In rapidly proliferating tumours, the number of fractions needed for tumour control increased exponentially with the probability of CSC symmetrical division, whereas in moderately growing HNC, this behaviour was linear. Severely hypoxic tumours could not be controlled by radiotherapy alone. Tumours with CSCs in a severely hypoxic niche required adjuvant therapies to be eradicated. CONCLUSIONS Growth kinetics strongly influence tumour responses to treatment. Slowly growing tumours showed linear dependence between dose and hypoxia/CSC, whereas rapidly growing tumours followed exponential behaviour.
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Affiliation(s)
- L G Marcu
- Faculty of Science, University of Oradea, Oradea, 410087, Romania.,School of Physical Sciences, The University of Adelaide, Adelaide, South Australia, 5005, Australia
| | - D Marcu
- Faculty of Science, University of Oradea, Oradea, 410087, Romania
| | - S M Filip
- Faculty of Science, University of Oradea, Oradea, 410087, Romania
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24
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Afenya EK, Ouifki R, Camara BI, Mundle SD. Mathematical modeling of bone marrow--peripheral blood dynamics in the disease state based on current emerging paradigms, part I. Math Biosci 2016; 274:83-93. [PMID: 26877072 DOI: 10.1016/j.mbs.2016.01.010] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2015] [Revised: 01/08/2016] [Accepted: 01/28/2016] [Indexed: 01/08/2023]
Abstract
Stemming from current emerging paradigms related to the cancer stem cell hypothesis, an existing mathematical model is expanded and used to study cell interaction dynamics in the bone marrow and peripheral blood. The proposed mathematical model is described by a system of nonlinear differential equations with delay, to quantify the dynamics in abnormal hematopoiesis. The steady states of the model are analytically and numerically obtained. Some conditions for the local asymptotic stability of such states are investigated. Model analyses suggest that malignancy may be irreversible once it evolves from a nonmalignant state into a malignant one and no intervention takes place. This leads to the proposition that a great deal of emphasis be placed on cancer prevention. Nevertheless, should malignancy arise, treatment programs for its containment or curtailment may have to include a maximum and extensive level of effort to protect normal cells from eventual destruction. Further model analyses and simulations predict that in the untreated disease state, there is an evolution towards a situation in which malignant cells dominate the entire bone marrow - peripheral blood system. Arguments are then advanced regarding requirements for quantitatively understanding cancer stem cell behavior. Among the suggested requirements are, mathematical frameworks for describing the dynamics of cancer initiation and progression, the response to treatment, the evolution of resistance, and malignancy prevention dynamics within the bone marrow - peripheral blood architecture.
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Affiliation(s)
- Evans K Afenya
- Department of Mathematics, Elmhurst College, 190 Prospect Avenue, Elmhurst, IL 60126, USA.
| | - Rachid Ouifki
- DST/NRF Centre of Excellence in Epidemiological Modelling and Analysis (SACEMA), Stellenbosch University, 19 Jonkershoek Rd, Stellenbosch, 7600, South Africa.
| | - Baba I Camara
- Laboratoire Interdisciplinaire des Environnements Continentaux, Universit de Lorraine, CNRS UMR 7360, 8 rue du General Delestraint, Metz 57070, France.
| | - Suneel D Mundle
- Department of Biochemistry, Rush University Medical Center, 1735 W. Harrison St, Chicago, IL 60612, USA.
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25
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Rodriguez-Brenes IA, Wodarz D, Komarova NL. Characterizing inhibited tumor growth in stem-cell-driven non-spatial cancers. Math Biosci 2015; 270:135-41. [PMID: 26344137 DOI: 10.1016/j.mbs.2015.08.009] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2014] [Accepted: 08/20/2015] [Indexed: 11/29/2022]
Abstract
Healthy human tissue is highly regulated to maintain homeostasis. Secreted negative feedback factors that inhibit stem cell division and stem cell self-renewal play a fundamental role in establishing this control. The appearance of abnormal cancerous growth requires an escape from these regulatory mechanisms. In a previous study we found that for non-solid tumors if feedback inhibition on stem cell self-renewal is lost, but the feedback on the division rate is still intact, then the tumor dynamics are characterized by a relatively slow sub-exponential growth that we called inhibited growth. Here we characterize the cell dynamics of inhibited cancer growth by modeling feedback inhibition using Hill equations. We find asymptotic approximations for the growth rates of the stem cell and differentiated cell populations in terms of the strength of the inhibitory signal: stem cells grow as a power law t(1/k+1),and the differentiated cells grow as t(1/k), where k is the Hill coefficient in the feedback law regulating cell divisions. It follows that as the tumor grows, undifferentiated cells take up an increasingly large fraction of the population. Implications of these results for specific cancers including CML are discussed. Understanding how the regulatory mechanisms that continue to operate in cancer affect the rate of disease progression can provide important insights relevant to chronic or other slow progressing types of cancer.
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Affiliation(s)
- Ignacio A Rodriguez-Brenes
- Department of Mathematics, University of California, Irvine, CA 92651, USA; Department of Ecology and Evolution, University of California, Irvine, CA 92651, USA.
| | - Dominik Wodarz
- Department of Mathematics, University of California, Irvine, CA 92651, USA; Department of Ecology and Evolution, University of California, Irvine, CA 92651, USA
| | - Natalia L Komarova
- Department of Mathematics, University of California, Irvine, CA 92651, USA; Department of Ecology and Evolution, University of California, Irvine, CA 92651, USA
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26
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Høyem MR, Måløy F, Jakobsen P, Brandsdal BO. Stem cell regulation: Implications when differentiated cells regulate symmetric stem cell division. J Theor Biol 2015; 380:203-19. [PMID: 25997796 DOI: 10.1016/j.jtbi.2015.05.009] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2014] [Revised: 01/30/2015] [Accepted: 05/05/2015] [Indexed: 01/04/2023]
Abstract
We use a mathematical model to show that if symmetric stem cell division is regulated by differentiated cells, then changes in the population dynamics of the differentiated cells can lead to changes in the population dynamics of the stem cells. More precisely, the relative fitness of the stem cells can be affected by modifying the death rate of the differentiated cells. This result is interesting because stem cells are less sensitive than differentiated cells to environmental factors, such as medical therapy. Our result implies that stem cells can be manipulated indirectly by medical treatments that target the differentiated cells.
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Affiliation(s)
| | - Frode Måløy
- Department of Computer Science, University of Stavanger, Norway
| | - Per Jakobsen
- Department of Mathematics and Statistics, University of Tromsø, Norway
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27
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Sidow A, Spies N. Concepts in solid tumor evolution. Trends Genet 2015; 31:208-14. [PMID: 25733351 DOI: 10.1016/j.tig.2015.02.001] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2014] [Revised: 02/01/2015] [Accepted: 02/01/2015] [Indexed: 01/14/2023]
Abstract
Evolutionary mechanisms in cancer progression give tumors their individuality. Cancer evolution is different from organismal evolution, however, and we discuss where concepts from evolutionary genetics are useful or limited in facilitating an understanding of cancer. Based on these concepts we construct and apply the simplest plausible model of tumor growth and progression. Simulations using this simple model illustrate the importance of stochastic events early in tumorigenesis, highlight the dominance of exponential growth over linear growth and differentiation, and explain the clonal substructure of tumors.
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Affiliation(s)
- Arend Sidow
- Departments of Pathology and of Genetics, Stanford University, Stanford, CA 94305, USA.
| | - Noah Spies
- Departments of Pathology and of Genetics, Stanford University, Stanford, CA 94305, USA
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28
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Abstract
At least several types of human haematological malignancies can now be seen as 'stem-cell diseases'. The best-studied in this context is acute myeloid leukaemia (AML). It has been shown that these diseases are driven by a pool of 'leukaemia stem cells (LSC)', which remain in the quiescent state, have the capacity to survive and self-renew, and are responsible for the recurrence of cancer after classical chemotherapy. It has been understood that LSC must be eliminated in order to cure patients suffering from haematological cancers. Recent advances in LSC research have allowed for description of LSC phenotype and identification of potential targets for anti-LSC therapies. This concise review summarises the current view on LSC biology and targeted approaches against LSC.
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29
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Lin SJ, Yang DR, Wang N, Jiang M, Miyamoto H, Li G, Chang C. TR4 nuclear receptor enhances prostate cancer initiation via altering the stem cell population and EMT signals in the PPARG-deleted prostate cells. Oncoscience 2015; 2:142-50. [PMID: 25859557 PMCID: PMC4381707 DOI: 10.18632/oncoscience.121] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2014] [Accepted: 02/06/2015] [Indexed: 12/13/2022] Open
Abstract
A recent report indicated that the TR4 nuclear receptor might suppress the prostate cancer (PCa) initiation via modulating the DNA damage/repair system. Knocking-out peroxisome proliferator-activated receptor gamma (PPARG), a nuclear receptor that shares similar ligands/activators with TR4, promoted PCa initiation. Here we found 9% of PCa patients have one allele of PPARG deletion. Results from in vitro cell lines and in vivo mouse model indicated that during PCa initiation TR4 roles might switch from suppressor to enhancer in prostate cells when PPARG was deleted or suppressed (by antagonist GW9662). Mechanism dissection found targeting TR4 in the absence of PPARG might alter the stem cell population and epithelial-mesenchymal transition (EMT) signals. Together, these results suggest that whether TR4 can enhance or suppress PCa initiation may depend on the availability of PPARG and future potential therapy via targeting PPARG to battle PPARG-related diseases may need to consider the potential side effects of TR4 switched roles during the PCa initiation.
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Affiliation(s)
- Shin-Jen Lin
- George Whipple Lab for Cancer Research, Departments of Pathology, Urology, Radiation Oncology, and The Wilmot Cancer Center, University of Rochester Medical Center, Rochester, NY, USA
| | - Dong-Rong Yang
- George Whipple Lab for Cancer Research, Departments of Pathology, Urology, Radiation Oncology, and The Wilmot Cancer Center, University of Rochester Medical Center, Rochester, NY, USA
| | - Nancy Wang
- George Whipple Lab for Cancer Research, Departments of Pathology, Urology, Radiation Oncology, and The Wilmot Cancer Center, University of Rochester Medical Center, Rochester, NY, USA
| | - Ming Jiang
- Department of Urologic Surgery, Vanderbilt-Ingram Comprehensive Cancer Center, Vanderbilt University Medical Center, Nashville, Tennessee, USA
| | - Hiroshi Miyamoto
- George Whipple Lab for Cancer Research, Departments of Pathology, Urology, Radiation Oncology, and The Wilmot Cancer Center, University of Rochester Medical Center, Rochester, NY, USA
| | - Gonghui Li
- George Whipple Lab for Cancer Research, Departments of Pathology, Urology, Radiation Oncology, and The Wilmot Cancer Center, University of Rochester Medical Center, Rochester, NY, USA ; Department of Urology, Sir Run Run Shaw Hospital, Zhejiang University, Hangzhou, China
| | - Chawnshang Chang
- George Whipple Lab for Cancer Research, Departments of Pathology, Urology, Radiation Oncology, and The Wilmot Cancer Center, University of Rochester Medical Center, Rochester, NY, USA
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30
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Abstract
This review discusses quantitative modeling studies of stem and non-stem cancer cell interactions and the fraction of cancer stem cells.
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Affiliation(s)
- Heiko Enderling
- Department of Integrated Mathematical Oncology
- H. Lee Moffitt Cancer Center & Research Institute
- Tampa
- USA
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Würstle ML, Zink E, Prehn JHM, Rehm M. From computational modelling of the intrinsic apoptosis pathway to a systems-based analysis of chemotherapy resistance: achievements, perspectives and challenges in systems medicine. Cell Death Dis 2014; 5:e1258. [PMID: 24874730 PMCID: PMC4047923 DOI: 10.1038/cddis.2014.36] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2013] [Revised: 12/20/2013] [Accepted: 01/02/2014] [Indexed: 12/14/2022]
Abstract
Our understanding of the mitochondrial or intrinsic apoptosis pathway and its role in chemotherapy resistance has increased significantly in recent years by a combination of experimental studies and mathematical modelling. This combined approach enhanced the quantitative and kinetic understanding of apoptosis signal transduction, but also provided new insights that systems-emanating functions (i.e., functions that cannot be attributed to individual network components but that are instead established by multi-component interplay) are crucial determinants of cell fate decisions. Among these features are molecular thresholds, cooperative protein functions, feedback loops and functional redundancies that provide systems robustness, and signalling topologies that allow ultrasensitivity or switch-like responses. The successful development of kinetic systems models that recapitulate biological signal transduction observed in living cells have now led to the first translational studies, which have exploited and validated such models in a clinical context. Bottom-up strategies that use pathway models in combination with higher-level modelling at the tissue, organ and whole body-level therefore carry great potential to eventually deliver a new generation of systems-based diagnostic tools that may contribute to the development of personalised and predictive medicine approaches. Here we review major achievements in the systems biology of intrinsic apoptosis signalling, discuss challenges for further model development, perspectives for higher-level integration of apoptosis models and finally discuss requirements for the development of systems medical solutions in the coming years.
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Affiliation(s)
- M L Würstle
- 1] Department of Physiology and Medical Physics, Royal College of Surgeons in Ireland, Dublin, Ireland [2] Centre for Systems Medicine, Royal College of Surgeons in Ireland, Dublin, Ireland
| | - E Zink
- 1] Department of Physiology and Medical Physics, Royal College of Surgeons in Ireland, Dublin, Ireland [2] Centre for Systems Medicine, Royal College of Surgeons in Ireland, Dublin, Ireland
| | - J H M Prehn
- 1] Department of Physiology and Medical Physics, Royal College of Surgeons in Ireland, Dublin, Ireland [2] Centre for Systems Medicine, Royal College of Surgeons in Ireland, Dublin, Ireland
| | - M Rehm
- 1] Department of Physiology and Medical Physics, Royal College of Surgeons in Ireland, Dublin, Ireland [2] Centre for Systems Medicine, Royal College of Surgeons in Ireland, Dublin, Ireland
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